The overarching goal of this proposal is to continue development and application of the class of stochastic models known as branching processes for various biological/biomedical applications, all of which involve cellular population dynamics. The models will be used to explain data, estimate parameters, assess specific hypotheses, and make predictions. Specific projects are (1) prion dynamics, (2) bacterial persistence, (3) telomere dynamics, (4) cell cycle desynchronization, (5) bacterial lag phase, and (6) Muller's ratchet of accumulation of deleterious mutations. There is a great need for mathematical modeling a quantitative data analysis biology in general and in cellular population dynamics in particular. Although different mathematical approaches have been taken to many of these problems, branching processes seem to offer significant improvement in that they are inherently stochastic, taking into account the natural random variation in cell cycle times, mutations, etc. They are also conceptually clear, starting from modeling behavior on the individual level, for example by modeling the cell cycle, and drawing conclusions based on population-level data. The proposed research is intended to have a direct impact on the biological applications mentioned above.